If the two right angles of a right triangle are A and B and the hypotenuse is C, then A 2+B 2 = C 2; That is to say, the sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse. There is also a deformation formula: AB= root sign (AC 2+BC 2), which is called the inverse theorem of Pythagorean theorem.

Data expansion:

The Book of Weekly Parallel Calculations records the situation of 1000 years BC. Taking (3,4,5) as an example, the quotient height explains the elements of Pythagorean theorem, proves that the square of chord length must be the sum of squares of two right-angled sides, and establishes the judgment principle that the sum of squares of two right-angled sides of a right-angled triangle is equal to the square of hypotenuse. Its judgment method is ignored because future generations don't know its method.

Egypt recorded (3, 4, 5) in papyrus in 2600 BC, and the largest Pythagorean array recorded in ancient Babylonian clay tablets was. There are more than 400 proofs of Pythagorean theorem, such as differential proof, area proof and so on.

In Nine Chapters Arithmetic Notes, Liu Hui used Pythagorean Theorem to find pi for many times, and used "digging and filling method" to make a "blue-black diagram" to complete the geometric proof of Pythagorean Theorem. There is still much debate about whether Pythagorean theorem has been discovered more than once.

Zhao Shuang Pythagorean Diagram Proof Method;

During the China Three Kingdoms period, Zhao Shuang made a Pythagorean square diagram, that is, a chord diagram, in order to prove Pythagorean theorem. According to its proof idea, its method can cover all right triangles, and it is a wordless proof method of Pythagorean theorem with oriental characteristics.

Liu Hui's certificate of "cutting and mending":

Liu Hui, a mathematician in Wei and Jin Dynasties in China, used his "digging and filling method" to make a "green Zhu diagram" to prove the Pythagorean theorem.

Use similar triangles's proof method:

There are many ways to prove Pythagorean theorem, all of which are based on the ratio of the lengths of two sides of similar triangles.

Euclid's proof:

1. If two triangles have two sets of corresponding sides and the angles between the two sets of sides are equal, then the two triangles are congruent. (SAS theorem)

2. The area of a triangle is half that of any parallelogram with the same base and height.

The area of any square is equal to the product of its two sides.

4. The area of any rectangle is equal to the product of its two sides (according to Auxiliary Theorem 3).

5. The idea of proof is to transform the two squares above into two rectangles with the same area below through a triangle with the same height and the same bottom.